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Johndcook

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Linear combination of sine and cosine as phase shift

  • A linear combination of sines and cosines can be written as a sine with a phase shift.
  • The calculation involves finding the values of A and φ.
  • For the case of a sin(x) + b cos(x) = A sin(x + φ):
  • If a and b are given, A = √(a² + b²) and φ = tan−1(b/a).

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